Abstract
We study the rheology of dry and wet granular materials in the steady quasistatic regime using the discrete element method in a split-bottom ring shear cell with focus on the macroscopic friction. The aim of our study is to understand the local rheology of bulk flow at various positions in the shear band, where the system is in critical state. We develop a general(ized) rheology, in which the macroscopic friction is factorized into a product of four functions, on top of the classical rheology, each of which depends on exactly one dimensionless control parameter, quantifying the relative importance of different micro-mechanical machanisms. These four control parameters relate the time scales of shear rate , particle stiffness tk, gravity tg and cohesion tc, respectively, with the governing time scale of confining pressure tp. While is large and thus of little importance for most of the slow flow data studied, it increases the friction in critical state, where the shear rate is high and decreases friction by relaxation (creep) where the shear rate is low. tg and tk are comparable to tp in the bulk, but become more or less dominant relative to tp at the extremes of low pressure at the free surface and high pressure deep inside the bulk, respectively. The effect of wet cohesion on the flow rheology is quantified by tc decreasing with increasing cohesion. Furthermore, the proposed rheological model predicts well the shear thinning behavior both in the bulk and near the free surface; shear thinning rate becomes less near the free surface with increasing cohesion.
Highlights
The ability to predict a material’s flow behavior, its rheology gives manufacturers an important product quantity
While the inertial number I [19], i.e. the ratio of confining pressure to strain-rate time scales, is used to describe the change in flow rheology from quasi-static to inertial conditions, we look at additional dimensionless numbers that influence the flow behavior. (i) The local compressibility p*, which is the squared ratio of the softness and stress time scales (ii) the inverse relative pressure gradient pg*, which is the squared ratio of gravitational and stress time scales and (iii) the Bond number Bo [48] quantifying local cohesion as the squared ratio of stress to wetting time scales are these dimensionless numbers
The critical state is achieved at a constant pressure and strain rate condition over regions with strain rate larger sthhaonwtehdetshtaratifnorrartoeta0t.i1ognmraaxt(ez0).a0s1shrposw, tnhiensfihgeuarreba3ncdorisrewspelolnesdtianbglitsohtehdearbeogvioenshoefasrhreaatrebgan>d.0W.0h1isle−[14, o0]f our analysis shown in the latter sections are in the shear band center is obtained by g > 0.8gmax (z) at different heights in the system
Summary
The ability to predict a material’s flow behavior, its rheology (like the viscosity for fluids) gives manufacturers an important product quantity. A frequent reason for the measurement of rheological properties can be found in the area of quality control, where raw materials must be consistent from batch to batch For this purpose, flow behavior is an indirect measure of product consistency and quality. The yield stress at critical state can be fitted as a linear function of the pressure with the friction coefficient of dry flow mo as the slope and a finite offset c, defined as the steady state cohesion in the limit of zero confining pressure [35]. This finite offset c is constant in the high pressure limit. Very little is known regarding the rheology for granular materials in the low pressure limit
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